On the Maxwell-Stefan approach to multicomponent diffusion

TL;DR

This paper analyzes the Maxwell-Stefan equations for multicomponent diffusion, proving local well-posedness by applying Perron-Frobenius theory to the governing matrix, thus advancing the mathematical understanding of complex diffusive systems.

Contribution

It introduces a novel application of Perron-Frobenius theory to establish ellipticity and well-posedness of the Maxwell-Stefan system for multicomponent diffusion.

Findings

Proved normal ellipticity of the diffusion operator

Established local-in-time well-posedness in isobaric, isothermal conditions

Applied Perron-Frobenius theorem to the flux-force matrix

Abstract

We consider the system of Maxwell-Stefan equations which describe multicomponent diffusive fluxes in non-dilute solutions or gas mixtures. We apply the Perron-Frobenius theorem to the irreducible and quasi-positive matrix which governs the flux-force relations and are able to show normal ellipticity of the associated multicomponent diffusion operator. This provides local-in-time wellposedness of the Maxwell-Stefan multicomponent diffusion system in the isobaric, isothermal case.